Susan Stepney.
The Art of Penrose Life.

Introduction

John Horton Conway’s Game of Life (GoL) is a simple two-dimensional,
two state cellular automaton (CA), remarkable for its complex behaviour.

The classic GoL is defined on a regular square lattice. The update rule depends
on the state of each cell and its neighbouring eight cells with which it shares a
vertex. Each cell has two states, ‘dead’ and ‘alive’. If a cell is alive at time t, then
it stays alive if and only if it has two or three live neighbours (otherwise it dies of
‘loneliness’ or ‘overcrowding’). If a cell is dead at time t, then it becomes alive (is
‘born’) if and only if it has exactly three live neighbours. This rule gives a famous
zoo of GoL patterns, including still lifes, oscillators, and gliders.

Here we show some results of running GoL rules on Penrose tilings. More detail
can be found in [127], from which all the figures here are taken. The neighbourhood
of a Penrose tile is again all the tiles with which it shares a vertex; now there can
be 7–11 of these, depending on details of the tiling. We show some interesting still
life patterns and oscillator patterns. For a fuller, but still preliminary, catalogue of
Penrose life structures, see [127]. These patterns were discovered by a combination
of systematic construction and random search.